# Topological Wave-Guiding Near an Exceptional Point: Defect-Immune, Slow-Light, Loss-Immune Propagation

## TL;DR

This paper explores a novel topological waveguide system combining non-Hermitian physics and topological photonics, enabling defect-immune, slow-light, and loss-immune wave propagation near an exceptional point.

## Contribution

It introduces the first theoretical analysis of coupled topological modes at an exceptional point in a non-Hermitian, non-reciprocal waveguide using Green's function theory.

## Key findings

- Achieves defect-immune wave propagation at discontinuities
- Demonstrates low group velocity near exceptional points
- Shows immunity to losses in the proposed system

## Abstract

Electromagnetic waves propagating, at finite speeds, in conventional wave-guiding structures are reflected by discontinuities and decay in lossy regions. In this Letter, we drastically modify this typical guided-wave behavior by combining concepts from non-Hermitian physics and topological photonics. To this aim, we theoretically study, for the first time, the possibility of realizing an exceptional point between \emph{coupled topological modes in a non-Hermitian non-reciprocal waveguide}. Our proposed system is composed of oppositely-biased gyrotropic materials (e.g., biased plasmas or graphene layers) with a balanced loss/gain distribution. To study this complex wave-guiding problem, we put forward an exact analysis based on classical Green's function theory, and we illustrate the behavior of coupled topological modes and the nature of their non-Hermitian degeneracies. We find that, by operating near an exceptional point, we can realize anomalous topological wave propagation with, at the same time, low group-velocity, inherent immunity to back-scattering at discontinuities, and immunity to losses. These theoretical findings may open exciting research directions and stimulate further investigations of non-Hermitian topological waveguides to realize robust wave propagation in practical scenarios.